How do you change an oxygen sensor on a 1999 Mazda miata mx5?

I just changed it (the front O2 sensor) on my 2003 Miata. I believe yours will be the same. First, you will need an O2 sensor wrench (about $10 from Advance Auto Parts). Don't waste your time trying to remove it without one. Then follow these steps:

1. Warm the engine, and let it cool to the point you can safely touch the sensor and exhaust pipe.
2. Jack up drivers side front wheel, and put a jack stand under the frame.
3. Remove wheel. (I put the wheel with a piece of 2 x 6 on top of it to the rear of the jack point for added safety.)
4. Apply Liquid Wrench or equivalent to the sensor-exhaust connection - wait at least five minutes.
5. You may still need to add a piece of pipe (or 1/2" spark plug socket with 8" extension worked for me) to your 3/8" ratchet wrench handle to get enough leverage to break the sensor free.
6. If you replace with a universal type O2 sensor (I used a Bosch 15733 sensor from Amazon at $45.41), you will need to reuse your old electrical connector by splicing it in. The Bosch unit I used has a special connector assembly for doing this. It is a bit tedious to assemble but seems very solid. Just follow the instructions. With the Bosch sensor, the two white and two black wires individually (two connections) go together and the remaining the single black and blue and single grey and white wires connect.
7. Reassemble.

You will need to remove the positive battery terminal to clear the check engine light.